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JEE Main 20127 MayOnline

Exam: JEE Main
Year: 2012
Date: 7 May
Mode: Online
Subject: Mathematics
Chapter: Straight Lines

JEE Main 2012 · 7 May · Online · Mathematics · Straight Lines

If the straight lines x+3 y=4,3 x+y=4 and x+y =0 form a triangle,...

If the straight lines

x+3 y=4,3 x+y=4

and

x+y

=0

form a triangle, then the triangle is

Options

Ascalene
Bequilateral triangle
Cisosceles
Dright angled isosceles

Correct answer

C. isosceles

Step-by-step solution

Let equation of

A B: x+3 y=4

Let equation of

B C: 3 x+y=4

Let equation of

C A: x+y=0

Now, By solving these equations we get

A=(-2,2), B=(1,1)

and

C=(2,-2)

Now,

A B=\sqrt{9+1}=\sqrt{10}

, B C=

\sqrt{1+9}=\sqrt{10}

and

C A=\sqrt{16+16}=\sqrt{32}

Since, length of

A B

and

B C

are same therefore triangle is isosceles.

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